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%I #16 Sep 08 2022 08:44:55
%S 29,88,205,703,40979,123640,288259,988417,57616445,173837752,
%T 405291949,1389713599,81008680691,244415755672,569840192035,
%U 1953936331777,113898147435101,343648378637080,801194904709261
%N Numerators of continued fraction convergents to sqrt(858).
%H Vincenzo Librandi, <a href="/A042656/b042656.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1406, 0, 0, 0, -1).
%F G.f.: (29 +88*x +205*x^2 +703*x^3 +205*x^4 -88*x^5 +29*x^6 -x^7)/(1 -1406*x^4 +x^8). - _Vincenzo Librandi_, Nov 30 2013
%F a(n) = 1406*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 30 2013
%t Numerator[Convergents[Sqrt[858], 30]] (* or *) CoefficientList[Series[(29 + 88 x + 205 x^2 + 703 x^3 + 205 x^4 - 88 x^5 + 29 x^6 - x^7)/(1 - 1406 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 30 2013 *)
%t LinearRecurrence[{0,0,0,1406,0,0,0,-1},{29,88,205,703,40979,123640,288259,988417},20] (* _Harvey P. Dale_, Mar 01 2019 *)
%o (Magma) I:=[29, 88, 205, 703, 40979, 123640, 288259, 988417]; [n le 8 select I[n] else 1406*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 30 2013
%Y Cf. A042657.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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